Quantum Correlation of Quantum Networks Based on Their Covariance Matrices
The characteristics of a quantum network are determined by the topology of the network and quantum states shared between nodes.In this paper,we establish a mathematical framework for quantum networks based on directed acyclic graphs.We provide a method for constructing the covariance matrix of a quantum network based on probability tensors,and obtain relevant properties of the covariance matrix.We further constructed a covariance matrix of a quantum network with respect to some quantum measurement.By defining a block coherence measure of the covariance matrix,we obtain a correlation measure of quantum networks.We proved that quantum correlation of quantum networks is 0 if and only if all shared states of the network are product states.
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